Merge pull request #1484 from rrtheonlyone/knapsack-exercise

Knapsack: Proposal for new exercise

exercises/knapsack/canonical-data.json

@@ -0,0 +1,116 @@
+{
+  "exercise": "knapsack",
+  "version": "1.0.0",
+  "comments": [
+    "Depending on the language, the input type can be modified"
+  ],
+  "cases": [
+    {
+      "description": "no items",
+      "property": "maximumValue",
+      "input": {
+        "maximumWeight": 100,
+        "items": {}
+      },
+      "expected": 0
+    },
+    {
+      "description": "one item, too heavy",
+      "property": "maximumValue",
+      "input": {
+        "maximumWeight": 10,
+        "items": [
+          { "weight": 100, "value": 1 }
+        ]
+      },
+      "expected": 0
+    },
+    {
+      "description": "five items (cannot be greedy by weight)",
+      "property": "maximumValue",
+      "input": {
+        "maximumWeight": 10,
+        "items": [
+          { "weight": 2, "value": 5 },
+          { "weight": 2, "value": 5 },
+          { "weight": 2, "value": 5 },
+          { "weight": 2, "value": 5 },
+          { "weight": 10, "value": 21 }
+        ]
+      },
+      "expected": 21
+    },
+    {
+      "description": "five items (cannot be greedy by value)",
+      "property": "maximumValue",
+      "input": {
+        "maximumWeight": 10,
+        "items": [
+          { "weight": 2, "value": 20 },
+          { "weight": 2, "value": 20 },
+          { "weight": 2, "value": 20 },
+          { "weight": 2, "value": 20 },
+          { "weight": 10, "value": 50 }
+        ]
+      },
+      "expected": 80
+    },
+    {
+      "description": "example knapsack",
+      "property": "maximumValue",
+      "input": {
+        "maximumWeight": 10,
+        "items": [
+          { "weight": 5, "value": 10 },
+          { "weight": 4, "value": 40 },
+          { "weight": 6, "value": 30 },
+          { "weight": 4, "value": 50 }
+        ]
+      },
+      "expected": 90
+    },
+    {
+      "description": "8 items",
+      "property": "maximumValue",
+      "input": {
+        "maximumWeight": 104,
+        "items": [
+          { "weight": 25, "value": 350 },
+          { "weight": 35, "value": 400 },
+          { "weight": 45, "value": 450 },
+          { "weight": 5, "value": 20 },
+          { "weight": 25, "value": 70 },
+          { "weight": 3, "value": 8 },
+          { "weight": 2, "value": 5 },
+          { "weight": 2, "value": 5 }
+        ]
+      },
+      "expected": 900
+    },
+    {
+      "description": "15 items",
+      "property": "maximumValue",
+      "input": {
+        "maximumWeight": 750,
+        "items": [
+          { "weight": 70, "value": 135 },
+          { "weight": 73, "value": 139 },
+          { "weight": 77, "value": 149 },
+          { "weight": 80, "value": 150 },
+          { "weight": 82, "value": 156 },
+          { "weight": 87, "value": 163 },
+          { "weight": 90, "value": 173 },
+          { "weight": 94, "value": 184 },
+          { "weight": 98, "value": 192 },
+          { "weight": 106, "value": 201 },
+          { "weight": 110, "value": 210 },
+          { "weight": 113, "value": 214 },
+          { "weight": 115, "value": 221 },
+          { "weight": 118, "value": 229 },
+          { "weight": 120, "value": 240 }
+        ]
+      },
+      "expected": 1458
+    }
+  ]
+}

exercises/knapsack/description.md

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+In this exercise, let's try to solve a classic problem.
+
+Bob is a thief. After months of careful planning, he finally manages to
+crack the security systems of a high-class apartment.
+
+In front of him are many items, each with a value (v) and weight (w). Bob,
+of course, wants to maximize the total value he can get; he would gladly
+take all of the items if he could. However, to his horror, he realizes that
+the knapsack he carries with him can only hold so much weight (W).
+
+Given a knapsack with a specific carrying capacity (W), help Bob determine
+the maximum value he can get from the items in the house. Note that Bob can
+take only one of each item.
+
+All values given will be strictly positive. Items will be represented as a
+list of pairs, `wi` and `vi`, where the first element `wi` is the weight of
+the *i*th item and `vi` is the value for that item.
+
+For example:
+
+Items: [
+  { "weight": 5, "value": 10 },
+  { "weight": 4, "value": 40 },
+  { "weight": 6, "value": 30 },
+  { "weight": 4, "value": 50 }
+]
+
+Knapsack Limit: 10
+
+For the above, the first item has weight 5 and value 10, the second item has
+weight 4 and value 40, and so on.
+
+In this example, Bob should take the second and fourth item to maximize his
+value, which, in this case, is 90. He cannot get more than 90 as his
+knapsack has a weight limit of 10.

exercises/knapsack/metadata.yml

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+---
+blurb: "Given a knapsack that can only carry a certain weight, determine which items to put in the knapsack in order to maximize their combined value."
+source: "Wikipedia"
+source_url: "https://en.wikipedia.org/wiki/Knapsack_problem"